Wigner approach to quantum transport in graded semiconductors

Graded electron bandstructures have long being used to beneficially influence the performance and functionality of electronic devices. In this work, we have developed a consistent fully quantum description of electron transport in terms of the Wigner distribution function, making use of the symmetric and hermitian effective-mass-like single band Hamiltonian that can be unambiguously constructed for graded systems. The generalized Wigner equation includes contributions that, in the quasiclassical limit, can be interpreted as directly corresponding to the drift and diffusion terms, but, unlike the homogeneous materials, the velocity operator is coordinate dependent and the electron is subject to the influence of the k-dependent quasielectric fields originating from both the inhomogeneous potential profile and composition-dependent modulation of the quasiparticle inertia. The approach is useful for the analysis of a broad class of transport phenomena in graded systems, where quantum effects are important, but a full quantum treatment would be prohibitively costly.